Cannot vs. Can Not

Because I have been reading, commenting, and correcting papers and theses for two days straight at work, and because of the extraordinary cumulation of people (one a fairly good writer of scientific English) I had to tell the following during that time; furthermore, because this has left me little time to do anything worthwhile to report in my blog, I want to reiterate:

“Cannot” and “can not” do not mean the same. “Cannot do” means that you are unable to do something. “Can not do” means that you are able to refrain from doing something. So “cannot” and “can not” cannot be used interchangeably.